Complex frequencies of a massless scalar field in loop quantum black hole spacetime

Chen Ju-Hua(陈菊华)^{†} and Wang Yong-Jiu(王永久)

College of Physics and Information Science, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control at the Ministry of Education, Hunan Normal University, Changsha 410081, China

Abstract Recently, considerable progress has been made in understanding the early universe by loop quantum cosmology. Modesto et al. investigated the loop quantum black hole (LQBH)using improved semiclassical analysis and they found that the LQBH has two horizons, an event horizon and a Cauchy horizon, just like the Reissner--Nordström black hole. This paper focuses on the dynamical evolution of a massless scalar wave in the LQBH background. By investigating the relation between the complex frequencies of the massless scalar field and the LQBH parameters using the numerical method, we find that the polymeric parameter P makes the massless scalar field decay more quickly and makes the ground scalar wave oscillate slowly. However, the polymeric parameter P causes the frequency of the high harmonic massless scalar wave to shift according to its value. We also find that the loop quantum gravity area gap parameter a_{0} causes the massless scalar field to decay more slowly and makes the period of the massless scalar field wave become longer. In the complex ω plane, the frequency curves move counterclockwise when the polymeric parameter P increases and this spiral effect is more obvious for a higher harmonic scalar wave.

Fund: Project supported Project supported by the National Natural Science Foundation of China (Grant No. 10873004), the Program for Excellent Talents at Hunan Normal University, China, the National Basic Research Program of China (Grant No. 2010CB832803), the Key Program of the National Natural Science Foundation of China (Grant No. 10935013), the Construct Program of the National Key Discipline, and the Program for Changjiang Scholars and the Innovative Research Team in University, China (Grant No. IRT0964).

Cite this article:

Chen Ju-Hua(陈菊华) and Wang Yong-Jiu(王永久) Complex frequencies of a massless scalar field in loop quantum black hole spacetime 2011 Chin. Phys. B 20 030401

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